Method for continuously measuring surface temperature of heated steel strip

ABSTRACT

A method for continuously measuring the surface temperature of a heated steel strip, includes providing a flat reflecting plate so as to face a heated steel strip at an angle of inclination (α) with the steel strip. A radiation thermometer measures the amount of heat radiation energy which is emitted from an arbitrary point on the surface of the steel strip and comes directly into the radiation thermometer; and the thermometer also measures the total sum of heat radiation energy which (a) is emitted from a different point on the surface of the steel strip and comes into the radiation thermometer after having been reflected at least twice between the steel strip and the reflecting plate and, (b) is emitted from a final reflecting point, on the steel strip, of the heat radiation from said different point. The emissivity of the steel strip is computed on the basis of said total sum of the energies of the heat radiations and the amount of energy of the heat radiation from the arbitrary point; and the surface temperature of the steel strip is measured on the basis of the computed emissivity and the amount of energy of a reference heat radiation. The final angle of reflection (θ) from the steel strip of the heat radiation from said different point, and the angle of inclination (α) of the reflecting plate, are set at values which satisfy specific limits.

REFERENCE TO PATENTS, APPLICATIONS AND PUBLICATIONS PERTINENT TO THEINVENTION

As far as is known, the only document pertinent to the present inventionis a paper entitled "A Method for Simultaneous Measurement of BothTemperature and Emissivity, and Its Applications to Steel Processes",released in the technical journal "Tetsu-to-Hagane" (which means "Ironand Steel") and published in Japan on Jan. 1, 1979.

The contents disclosed in the above-mentioned prior art document will bediscussed later under the heading of the "BACKGROUND OF THE INVENTION".

FIELD OF THE INVENTION

The present invention relates to a method for continuously measuring thesurface temperature of a heated steel strip utilizing heat radiationsemitted from the surface of the heated steel sheet.

BACKGROUND OF THE INVENTION

When continuously heating a steel strip in a heating furnace, forexample, measurement of the surface temperature of the steel stripheated in the heating furnace is very important in controlling theheating operation of the steel strip in the heating furnace.

The surface temperature of a heated steel strip is generally measuredwith a radiation thermometer, and accurate determination of emissivityof the surface of the steel strip is essential for the accuratemeasurement of the surface temperature of the steel strip.

A method for measuring the surface temperature of a heated steel stripthrough calculation of the surface emissivity of the heated steel stripis disclosed in a paper entitled "A Method for Simultaneous Measurementof Both Temperature and Emissivity, and Its Applications to SteelProcesses", released in the technical journal "Tetsu-to-Hagane" (whichmeans "Iron and Steel") and published in Japan on Jan. 1, 1979(hereinafter referred to as the "prior art"). The prior art is describedbelow with reference to the drawings.

FIG. 1 is a descriptive front view illustrating the method for measuringthe surface temperature of a heated steel strip of the prior art, andFIG. 2 is a descriptive plan view of FIG. 1. As shown in FIGS. 1 and 2,a cylindrical reflecting plate 1 is vertically provided above thesurface of a heated steel strip 2, spaced apart from the surfacethereof. The inner surface of the cylindrical reflecting plate 1 isplated with gold so as to efficiently reflect heat radiation emittedfrom the surface of the steel strip 2. A radiation thermometer 3 isprovided above the cylindrical reflecting plate 1 and on the axial lineof the cylindrical reflecting plate 1. A rotary chopper 4 having a pairof slits 5 is horizontally provided adjacent to the top end of thecylindrical reflecting plate 1. The rotary chopper 4 rotates at aconstant speed by a motor 6 and opens and closes the upper opening ofthe cylindrical reflecting plate 1.

As shown in FIG. 3(a), when the rotary chopper 4 opens the upper openingof the cylindrical reflecting plate 1, an amount of energy E₁ of a heatradiation which is emitted from a point P on the surface of the steelstrip 2 and comes directly into the radiation thermometer 3, is measuredby the radiation thermometer 3. Then, as shown in FIG. 3(b), when therotary chopper 4 closes the upper opening of the cylindrical reflectingplate 1, the total sum E₂ of the amount of energy E₁ of the heatradiation emitted from the point P and an amount of energy of a heatradiation which is emitted also from the point P and comes into theradiation thermometer 3 through the slit 5 of the rotary chopper 4 afterhaving been reflected several times among the surface of the steel strip2, the inner surface of the cylindrical reflecting plate 1 and the innersurface of the rotary chopper 4, is measured by the radiationthermometer 3. The amount of energy E₂ is larger than the amount ofenergy E₁, and these are expressed by the following formulae:

    E.sub.1 =ε·E.sub.b (T)                    (1), and

    E.sub.2 =g(ε)·E.sub.b (T)                 (2)

where,

ε: emissivity of the surface of the steel strip 2,

E_(b) (T): amount of energy of heat radiation emitted from the surfaceof a perfect blackbody having a temperature T (in other words, E_(b) (T)means the amount of energy of a reference heat radiation), and

g(ε): apparent emissivity of the surface of the steel strip 2.

Since the amount of energy E₂ is larger than the amount of energy E₁, asdescribed above, the apparent emissivity g(ε) is larger than theemissivity ε. The emissivity ε can be calculated by the followingformula on the basis of the mutual reflection theory:

    g(ε)=ε(α+1)/(ε+α)      (3)

where,

α: constant dependent upon the shape and the reflection characteristicsof the cylindrical reflecting plate 1.

Therefore, Formula (2) can be expressed as follows:

    E.sub.2 =E.sub.b (T)·ε(α+1)/(ε+α) (4)

From Formulae (1) and (4), the emissivity ε can be expressed as follows:##EQU1##

From Formulae (1) and (5), E_(b) (T) can be expressed as follows:##EQU2##

In Formula (6), E₁, E₂ and α are known. It is therefore possible, bymeans of Formula (6), to calculate the amount of energy E_(b) (T) ofheat radiation emitted from the surface of the steel strip 2 on theassumption that the steel strip 2 is a perfect blackbody. Since thetemperature corresponding to the amount of energy E_(b) (T) ispreviously known, the surface temperature of the steel strip 2 can bedetermined from the amount of energy E_(b) (T).

The above-mentioned prior art involves however the following problems:Because of the complicated paths of reflection of the heat radiationamong the surface of the steel strip 2, the inner surface of thecylindrical reflecting plate 1 and the inner surface of the rotarychopper 4, it is impossible to calculate the number of reflections ofthe heat radiation, leading to complicated calculations for determiningthe surface temperature of the steel strip 2. In addition, because ofthe necessity of providing the rotary chopper 4 adjacent to the top endof the cylindrical reflecting plate 1, the temperature measuringapparatus requires a large space, resulting in restrictions on the siteof installation of the apparatus.

Under such circumstances, there has been a demand for the development ofa method allowing simpler measurement of the surface temperature of aheated steel strip and requiring a smaller space for the temperaturemeasuring apparatus, but such a method has not as yet been proposed.

SUMMARY OF THE INVENTION

An object of the present invention is therefore to provide a methodallowing simpler measurement of the surface temperature of a heatedsteel strip and requiring a smaller space for the temperature measuringapparatus, by making it possible to accurately calculate the number ofreflections of a heat radiation between the surface of the steel stripand that of the reflecting plate.

In accordance with one of the features of the present invention, thereis provided a method for continuously measuring the surface temperatureof a heated steel strip, which includes:

providing a flat reflecting plate so as to face a travelling heatedsteel strip, at a first angle of inclination with the steel strip;

directing a radiation thermometer at a second inclination angle relativeto the steel strip;

continuously measuring with the raidation thermometer the amount of heatradiation energy which is emitted from an arbitrary point on the surfaceof said steel strip and comes directly into said radiation thermometer;

continuously measuring with said radiation thermometer the total sum of

(a) an amount of heat radiation energy which is emitted from at leastone different point on the surface of said steel strip other than saidarbitrary point and comes into said radiation thermometer after havingbeen reflected at least twice between the surface of said steel stripand the surface of said reflecting plate, and

(b) the amount of heat radiation energy emitted from a pointcorresponding to a final reflection point, on the steel strip of theheat radiation from said at least one different point;

continuously calculating emissivity of the surface of said steel stripon the basis of the thus measured total sum of the amounts of energy ofthe heat radiations emitted from said at least one different point, andsaid amount of energy of said heat radiation emitted from said arbitrarypoint;

continuously measuring the surface temperature of said steel strip onthe basis of the thus calculated emissivity and an amount of energy of areference heat radiation emitted from the surface of a perfectblackbody; and

determining a final angle of reflection (θ) on the surface of the steelstrip of said heat radiation emitted from said at least one differentpoint and reflected at least twice between the steel strip surface andthe surface of the flat reflecting plate, and said prescribed angle ofinclination (α) of said reflecting plate with said steel strip at valueswhich satisfy the following limits:

    40°≦θ<90°                       (A); and

    40°≦θ+2α≦140°      (B).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a descriptive front view illustrating the method for measuringthe surface temperature of a heated steel strip of the prior art;

FIG. 2 is a descriptive plan view of FIG. 1;

FIG. 3(a) is a descriptive front view illustrating the path of anincident heat radiation coming into a radiation thermometer from thesurface of a heated steel strip when opening the upper opening of acylindrical reflecting plate in the prior art;

FIG. 3(b) is a descriptive front view illustrating the paths of anincident heat radiation coming through a slit of a cylindricalreflecting plate into a radiation thermometer from the surface of aheated steel strip when closing the upper opening of the cylindricalreflecting plate in the prior art;

FIG. 4 is a descriptive front view illustrating the first embodiment ofthe method of the present invention;

FIG. 5 is a graph illustrating the relation between an angle ofinclination θ of a radiation thermometer with the surfaces of varioussteel strips and an emissivity ε of the surface of each of the varioussteel strips calculated on the basis of an amount of energy of a heatradiation which is emitted from the surface of each of the various steelstrips and comes directly into the radiation thermometer;

FIG. 6 is a graph illustrating the region for setting an angle ofinclination α of a reflecting plate and an angle of inclination θ of aradiation thermometer in the first embodiment of the method of thepresent invention as shown in FIG. 4.

FIG. 7 is a descriptive front view illustrating another mode of moving areflecting plate in the first embodiment of the method of the presentinvention as shown in FIG. 4;

FIG. 8 is a descriptive front view illustrating the principle of thesecond embodiment of the method of the present invention;

FIG. 9 is a descriptive front view illustrating the paths of heatradiations when the heat radiations emitted from points on the surfaceof the steel strip are reflected a plurality of times between thesurface of the reflecting plate and that of the steel strip and thencome into the radiation thermometer in the second embodiment of themethod of the present invention;

FIG. 10 is a graph illustrating, in the case with an angle ofinclination θ of 60° of a radiation thermometer, the relation among anangle of inclination α of a reflecting plate, a ratio d/l of thedistance d between an end of the reflecting plate and the surface of asteel strip to the length l of the reflecting plate, and a number ofreflection n of a heat radiation emitted from a point on the surface ofthe steel strip between the surface of the steel strip and that of thereflecting plate in the second embodiment of the method of the presentinvention;

FIG. 11 is a graph illustrating, in the case with an angle ofinclination θ of 70° of a radiation thermometer, the relation among saidangle of inclination α of a reflecting plate, said ratio d/l, and saidnumber of reflection n in the second embodiment of the method of thepresent invention; and

FIG. 12 is a graph illustrating the region for setting an angle ofinclination α of a reflecting plate and an angle of inclination θ of aradiation thermometer in the second embodiment of the method of thepresent invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

From the point of view as mentioned above, extensive studies werecarried out to develop a method allowing simpler measurement of thesurface temperature of a heated steel strip and requiring a smallerspace for the temperature measuring apparatus. As a result, thefollowing findings were obtained: By providing a flat reflecting plateso as to face a heated steel strip at a prescribed angle of inclinationwith the steel sheet, it is possible to easily calculate the number ofreflections of a heat radiation between the surface of the steel stripand that of the reflecting plate, and consequently, it is possible tosimple measure the surface temperature of the steel strip and to achievea compact temperature measuring apparatus.

The present invention was conceived on the basis of the above-mentionedfindings. The method for continuously measuring a surface temperature ofa heated steel strip of the present invention is described below withreference to the drawings.

FIG. 4 is a descriptive front view illustrating the first embodiment ofthe method of the present invention. As shown in FIG. 4, a flatreflecting plate 1 is provided below a horizontally travelling heatedsteel strip 2 spaced apart from the surface thereof so as to face thesteel strip 2 at a prescribed angle of inclination α with the steelstrip 2. The line formed by the intersection of the extended plane ofthe reflecting plate 1 with the surface of the steel strip 2 is normalto the plane of the drawing, i.e., substantially perpendicular to thetravelling direction of the steel strip 2. The reflecting plate 1 ismade of aluminum or other materials having a known reflectivity. Aradiation thermometer 3 measures an amount of energy of a heat radiationwhich is emitted from the surface of the steel strip 2 and comes intothe radiation thermometer 3 along the optical axis thereof. Theradiation thermometer 3 is provided at an angle with the steel strip 2so that the angle between the optical axis of the radiation thermometer3 passing through a point A on the surface of the steel strip 2 and thesurface of the steel strip 2 becomes θ, with a prescribed distance tothe steel strip 2, on the side of end O' of the reflecting plate 1 whichhas a longer distance from the steel strip 2 than the other end O of thereflecting plate 1. Therefore, a heat radiation emitted from anotherpoint C on the surface of the steel strip 2 apart from the point A by aprescribed distance is reflected at a point B on the surface of thereflecting plate 1, and then reflected at the point A with an angle ofreflection θ_(A) (equal to θ) to come into the radiation thermometer 3.A moving device 7 reciprocally moves the reflecting plate 1 in thelongitudinal direction thereof between the position at which the heatradiation emitted from the point C on the surface of the steel strip 2is reflected at the point B on the surface of the reflecting plate 1,and a position not reflecting this heat radiation. A computer 8calculates the surface temperature of the steel strip 2 on the basis ofthe amount of energy of a heat radiation which is emitted from thesurface of the steel strip 2, directly or after reflection into theradiation thermometer 3, and is measured thereby.

When the reflecting plate 1 is moved by the moving device 7 to aposition where the heat radiation emitted from the point C on thesurface of the steel strip 2 is not reflected at the point B on thesurface of the reflecting plate 1, only the heat radiation emitted fromthe point A on the surface of the steel strip 2 comes into the radiationthermometer 3. At this moment, the amount of energy E₁ of the heatradiation measured by the radiation thermometer 3 is expressed asfollows:

    E.sub.1 =ε.sub.1 ·E.sub.b (T.sub.1)       (7)

In addition to moving the reflecting plate 1 in the longitudinaldirection thereof as shown in FIG. 4, the moving device 7 mayalternately rotate the reflecting plate 1 between the position at whichthe heat radiation emitted from the point C on the surface of the steelstrip 2 is reflected at the point B on the surface of the reflectingplate 1, and the position at which said heat radiation is not reflected,as shown in FIG. 7.

When the reflecting plate 1 is moved by the moving device 7 to theposition where the heat radiation emitted from the point C on thesurface of the steel strip 2 is reflected at the point B on the surfaceof the reflecting plate 1, the heat radiation emitted from the point Con the surface of the steel strip 2, the heat radiation emitted from thepoint B on the surface of the reflecting plate 1, and the heat radiationemitted from the point A on the surface of the steel strip 2 comerespectively into the radiation thermometer 3. The amounts of energy ofheat radiations measured by the radiation thermometer 3 are expressed bythe following formula:

    E.sub.2 =ε.sub.1 ·E.sub.b (T.sub.1)+ε.sub.2 ·r.sub.1 ·E.sub.b (T.sub.2)+ε.sub.1 ·r.sub.1 ·r.sub.2 ·E.sub.b (T.sub.1) (8)

In Formulae (7) and (8),

ε₁ : emissivity of the surface of the steel strip 2,

ε₂ : emissivity of the surface of the reflecting plate 1,

r₁ : reflectivity of the surface of the steel strip 2,

r₂ : reflectivity of the surface of the reflecting plate 1,

E_(b) (T₁): amount of energy of the heat radiation emitted from thesurface of a perfect blackbody at temperature T₁ (i.e., amount of energyof reference heat radiation at temperature T₁),

E_(b) (T₂): amount of energy of the heat radiation emitted from thesurface of a perfect blackbody at temperature T₂ (i.e., amount of energyof reference heat radiation at temperature T₂).

In Formula (8), the first term of the right side expresses the amount ofenergy of the heat radiation which is emitted from the point A on thesurface of the steel strip 2 and comes directly into the radiationthermometer 3; the second term of the right side expresses the amount ofenergy of the heat radiation which is emitted from the point B on thesurface of the reflecting plate 1 and comes into the radiationthermometer 3 after the reflection at the point A on the surface of thesteel strip 2; and the third term of the right side expresses the amountof energy of the heat radiation which is emitted from the point C on thesurface of the steel strip 2 and comes into the radiation thermometer 3after the reflections at the points B and A.

When the surface temperature of the reflecting plate 1 is considerablylower than that of the steel strip 2, this results in: E_(b) (T₁)>>E_(b)(T₂) in Formula (8), and the second term of the right side of Formula(8) is negligible. Formula (8) can therefore be simplified as follows:

    E.sub.2 ≈ε.sub.1 (1+r.sub.1 ·r.sub.2)·E.sub.b (T.sub.1)             (9)

Thus, the following formula can be derived from Formulae (7) and (9):

    E.sub.2 /E.sub.1 =1+r.sub.1 ·r.sub.2              (10)

If, on the assumption of E₂ /E₁ =k, Kirchhoff's law, i.e., the law thatthe sum of emissivity and reflectivity is equal to 1, is applied here,the emissivity ε₁ of the surface of the steel strip 2 can be expressedby the following formula since the reflectivity r₂ of the reflectingplate 1 is known: ##EQU3##

After calculation of the emissivity ε₁ of the surface of the steel strip2 by Formula (11), it is possible to calculate the surface temperatureof the steel strip 2 from Formula (7). All these calculations areperformed by the computer 8.

Now, the relation between the angle of inclination θ of the radiationthermometer 3 and the angle of inclination α of the reflecting plate 1is described below, which gives the number of reflection of twice of theheat radiation emitted from the point C on the surface of the steelstrip 2 between the surface of the steel strip 2 and the surface of thereflecting plate 1, and which can minimize measuring error of thesurface temperature of the steel strip 2.

FIG. 5 is a graph illustrating the relation between an angle ofinclination θ of the radiation thermometer 3 with the surfaces ofvarious steel strips and an emissivity ε of the surface of each of thevarious steel strips calculated on the basis of an amount of energy of aheat radiation which is emitted from the surface of each of the varioussteel strips and comes directly into the radiation thermometer 3. As isclear from FIG. 5, so far as the angle of inclination θ of the radiationthermometer 3 satisfies the condition: 40°≦θ<90°, the measured values ofthe emissivity ε are kept almost constant even when the angle ofinclination θ of the radiation thermometer 3 varies within this range.On the other hand, when the angle of inclination θ of the radiationthermometer 3 is under 40°, the measured values of the emissivity ε varyaccording as the angle of inclination θ of the radiation thermometer 3varies. In view of this fact, the angles of reflection θ_(A), θ_(C) andθ_(B) of the heat radiation at the points A and C on the surface of thesteel strip 2 and at the point B on the surface of the reflecting plate1 in FIG. 4 must satisfy the following condition:

    40°≦θ.sub.A, θ.sub.B, θ.sub.C <90°(12)

The reason is as follows: The emissivity ε₁ of the surface of the steelstrip 2 is calculated by Formula (11) on the assumption that the surfaceof the steel strip 2 has the same emissivity at the points A and C. Asdescribed above, however, the measured values of the emissivity ε varywith an angle of inclination θ of the radiation thermometer 3 of under40°. This causes an error in the calculation of the emissivity ε₁ byFormula (11), leading to a decreased measuring accuracy of the surfacetemperature of the steel strip 2.

On the assumption that the heat radiation is specularly reflected on thesurface of the steel strip 2 and on the surface of the reflecting plate1, these angles of reflection θ_(A), θ_(B) and θ_(C) are expressed asfollows:

    θ.sub.A =θ                                     (13),

    θ.sub.B =θ+α                             (14),

where, (θ+α)<90°

    θ.sub.B =180°-(θ+α)               (15),

where, (θ+α)>90°

    θ.sub.C =θ+2α                            (16), and

where, (θ+2α)<90°

    θ.sub.C =180°-(θ+2α)              (17),

where, (θ+2α)>90°

As is concluded from Formulae (12), (13), (14), (15), (16) and (17), inorder to give the number of reflection of twice of the heat radiationemitted from the point C on the surface of the steel strip 2 between thesurface of the steel strip 2 and the surface of the reflecting plate 1,and for the angles of reflection θ_(A), θ_(B) and θ_(C) to satisfyFormula (12), it is necessary for the angle of inclination α of thereflecting plate 1 and the angle of inclination θ of the radiationthermometer 3 to satisfy the following formulae:

    40°≦θ<90°                       (A), and

    40°≦θ+2α≦140°      (B)

FIG. 6 illustrates the region for setting the angle of inclination α ofthe reflecting plate 1 and the angle of inclination θ of the radiationthermometer 3, enclosed by straight lines defined by Formulae (A) and(B) in the first embodiment of the method of the present invention.

The first embodiment of the method of the present invention describedabove is particularly effective when measuring the surface temperatureof a steel strip having a relatively high emissivity.

Now, the second embodiment of the method of the present invention whichpermits highly accurate and easy measurement of the surface temperatureof a steel strip having a relatively low emissivity is described belowwith reference to the drawings.

FIG. 8 is a descriptive front view illustrating the principle of thesecond embodiment of the method of the present invention. As shown inFIG. 8, a flat reflecting plate 1 is provided below a horizontallytravelling heated steel strip 2 spaced apart from the surface thereof soas to face the steel strip 2 at a prescribed angle of inclination α withthe steel strip 2. The line formed by the intersection of the extendedplane of the reflecting plate 1 with the surface of the steel strip 2 isnormal to the plane of the drawing, i.e., substantially perpendicular tothe travelling direction of the steel strip 2. The reflecting plate 1 ismade of aluminum or other materials having a known reflectivity. Aradiation thermometer 3 measures an amount of energy of a heat radiationwhich is emitted from the surface of the steel strip 2 and comes intothe radiation thermometer 3 along the optical axis thereof. Theradiation thermometer 3 is provided, with a prescribed distance to thesteel strip 2, on the side of end O' of the reflecting plate 1 which hasa longer distance from the steel strip 2 than the other end O of thereflecting plate 1. A rotating device 9 alternately rotates theradiation thermometer 3 between a position at which the optical axis ofthe radiation thermometer 3 forms a right angle with the steel strip 2and the position at which the optical axis forms an angle of inclinationθ with the steel strip 2. A computer 8 calculates the surfacetemperature of the steel strip 2 on the basis of the amount of energy ofa heat radiation which is emitted from the surface of the steel strip 2,directly or after reflection into the radiation thermometer 3, and ismeasured thereby.

FIG. 9 is a descriptive front view illustrating the paths of heatradiations when the heat radiations emitted from points P₁ to P₁₃ on thesurface of the steel strip 2 are reflected a plurality of times betweenthe surface of the reflecting plate 1 and that of the steel strip 2, andthen come into the radiation thermometer 3 in the second embodiment ofthe method of the present invention. As shown in FIG. 9, a heatradiation emitted, for example, from the point P₁₃ would come, throughreflections at the points P₁₂, P₁₁ . . . P₁, into the radiationthermometer 3 if the surface of the steel strip 2 and the surface of thereflecting plate 1 are specularly reflecting surfaces. All the heatradiations emitted from the points P₁ to P₁₂ other than the point P₁₃also come into the radiation thermometer 3 through the paths mentionedabove.

When the radiation thermometer 3 is rotated by the rotating device 9 soas to form an angle of inclination of θ with the steel strip 2, theamount of energy E₁ of the heat radiations measured by the radiationthermometer 3 is expressed by the following formula: ##EQU4## where, ε₁: emissivity of the surface of the steel strip 2,

ε₂ : emissivity of the surface of the reflecting plate 1,

r₁ : reflectivity of the surface of the steel strip 2,

r₂ : reflectivity of the surface of the reflecting plate 1,

E_(b) (T₁): amount of energy of the heat radiation emitted from thesurface of a perfect blackbody at temperature T₁ (i.e., amount of energyof reference heat radiation at temperature T₁),

E_(b) (T₂): amount of energy of the heat radiation emitted from thesurface of a perfect blackbody at temperature T₂ (i.e., amount of energyof reference heat radiation at temperature T₂),

n₁ : number of reflection of the heat radiation on the surface of thesteel strip 2,

n₂ : number of reflection of the heat radiation on the surface of thereflecting plate 1.

In Formula (18), the first term of the right side expresses the totalsum of the amounts of energy of heat radiations emitted from the surfaceof the steel strip 2; and the second term of the right side expressesthe total sum of the amounts of energy of heat radiations emitted fromthe surface of the reflecting plate 1.

In Formula (18), the numbers of reflection n₁ and n₂ can begeometrically determined in advance. When the sum of the numbers ofreflection n₁ and n₂, i.e., the number of reflection n of the heatradiation emitted from the point P₁₃ on the surface of the steel strip 2between the surface of the steel strip 2 and that of the reflectingplate 1 is set at a value of at least 10, it is possible to obtain asufficiently high apparent emissivity of the surface of the steel strip2 as described later. This ensures measurement at a higher accuracy ofthe surface temperature of the steel strip 2.

When the surface temperature of the reflecting plate 1 is considerablylower than that of the steel strip 2, this results in: E_(b) (T₁)>>E_(b)(T₂) in Formula (18), and the amount of energy E₁ of the heat radiationmeasured by the radiation thermometer 3 can be simplified as follows:##EQU5## where, g(ε): apparent emissivity of the surface of the steelstrip 2.

Then, the radiation thermometer 3 is rotated by the rotating device 9 sothat the optical axis of the radiation thermometer 3 forms a right anglewith the steel strip 2. In this case, the amount of energy E₂ of theheat radiation measured by the radiation thermometer 3 can be expressedby the following formula. If, in this case, damping of the amount ofenergy E₂ is negligible and an angle formed between the optical axis ofthe radiation thermometer 3 and the surface of the steel strip 2 is notaffected by the reflecting plate 1, this angle is not limited to 90°:

    E.sub.2 =ε.sub.1 ·E.sub.b (T.sub.1)       (20)

The following formula is derived from Formulae (19) and (20): ##EQU6##

In the Formula (21), if E₁ /E₂ =k, then Formula (21) can be rewritten asfollows:

    (r.sub.1 ·r.sub.2).sup.n 1-k·(r.sub.1 ·r.sub.2)+(k-1)=0                                (22)

In Formula (22), since n₁, r₂ and k are known as described above, it ispossible to calculate the reflectivity r₁ of the surface of the steelstrip 2 by solving Formula (22) by the pincers operation method, forexample. When the reflectivity r₁ of the surface of the steel strip 2can thus be calculated, it is then possible to calculate the emissivityε₁ of the surface of the steel strip 2 in accordance with Kirchhoff'slaw as mentioned above. When the emissivity ε₁ of the surface of thesteel strip 2 can thus be calculated, it is then possible to calculatethe surface temperature of the steel strip 2 by Formula (20). All thesecalculations are performed by the computer 8.

In Formula (22), since the value of r₁ ·r₂ satisfies the condition: 0<r₁·r₂ <1 when the number of reflection n of the heat radiation is at least10, the value of (r₁ ·r₂)^(n) 1 can be considered almost zero. FromFormula (22) and Kirchhoff's law described above, therefore, theemissivity ε₁ of the surface of the steel strip 2 can be calculated bythe following formula: ##EQU7##

Now, the relation between the angle of inclination θ of the radiationthermometer 3 and the angle of inclination α of the reflecting plate 1is described below, which can give the number of reflection n of atleast 10 of the heat radiation and which can minimize measuring errorsof the surface temperature of the steel strip 2.

FIG. 10 is a graph illustrating, in the case with an angle ofinclination θ of 60° of the radiation thermometer 3, the relation amongthe angle of inclination α of the reflecting plate 1, the ratio d/l ofthe distance d between an end O' of the reflecting plate 1 and thesurface of the steel strip 2 to the length l of the reflecting plate 1,and the number of reflection n of the heat radiation. FIG. 11 is a graphillustrating the relation among said angle of inclination α of thereflecting plate 1, said ratio d/l, and said number of reflection n inthe case with an angle of inclination θ of 70° of the radiationthermometer 3.

As shown in FIGS. 10 and 11, when the angle of inclination α of thereflecting plate 1 is at least 0°, the number of reflection n of theheat radiation becomes at least 10, irrespective of the ratio d/l. It isnecessary, as mentioned above, to set the angle of reflection of theheat radiation on the surface of the steel strip 2 and on the surface ofthe reflecting plate 1 at a value within the range of at least 40° andunder 90°. The relation between the angle of inclination θ of theradiation thermometer 3 and the angle of inclination α of the reflectingplate 1, which can give the number of reflection n of at least 10 of theheat radiation and at the same time satisfies the above-mentionedcondition for the angle of reflection, is expressed by the followingformulae:

    θ≦-4.5α+87                              (C),

where, 0°≦α≦9°

    θ≧-5α+60                                (D),

where, 0°≦α≦4°

    θ≧4α+24                                 (E), and

where, 4°≦α≦5°

    θ≧0.6α+41                               (F)

where, 5°≦α≦9°.

FIG. 12 illustrates the region for setting the angle of inclination α ofthe reflecting plate 1 and the angle of inclination θ of the radiationthermometer 3, enclosed by straight lines defined by Formulae (C), (D),(E) and (F).

The above description has covered the case where the radiationthermometer 3 is alternately rotated so that the optical axis thereofforms 90° with the steel strip 2, and then forms the angle ofinclination θ with the steel strip 2. Two radiation thermometers may beused by installing one with the optical axis thereof forming 90° withthe steel strip 2, and the other with the optical axis thereof formingthe angle of inclination θ with the steel strip 2.

According to the present invention, as described above, it is possibleto accurately determine the number of reflection of the heat radiationbetween the surface of the steel strip and that of the reflecting plate,and hence to easily perform calculation of the surface temperature ofthe steel strip, requiring a smaller space for the temperature measuringapparatus because of the elimination of the necessity to install arotary chopper as in the prior art.

What is claimed is:
 1. A method of continuously measuring a surfacetemperature of a travelling heated steel strip, whichcomprises:providing a flat reflecting plate at a prescribed position soas to face a travelling heated steel strip at a first inclination angle(α) relative to said steel strip, said first inclination angle (α) andsaid position of said reflecting plate being selectively changeable;directing a radiation thermometer for measuring an amount of energy of aheat radiation emitted from the surface of said steel strip toward saidsteel strip at a second inclination angle relative to said steel strip,said second inclination angle being selectively changeable; continuouslymeasuring with said radiation thermometer the amount of energy of a heatradiation which is emitted from an arbitrary point on the surface ofsaid steep strip and which heat radiation comes directly into saidradiation thermometer; continuously measuring with said radiationthermometer the total sum of the amount of energy of (a) a heatradiation which is emitted from at least one different point on thesurface of said steel strip other than said arbitrary point and whichcomes into said radiation thermometer after having been reflected atleast twice between the surface of said steel strip and the surface ofsaid flat reflecting plate and, (b) the amount of energy of a heatradiation which is emitted from a point on the surface of said steelstrip which point is a final reflecting point of the heat radiation fromsaid at least one different point, and which radiation comes directlyinto said radiation thermometer; continuously calculating emissivity ofthe surface of said steel strip on the basis of said total sum thusmeasured of the amounts of energy of the heat radiations (a) and (b),and said amount of energy of said heat radiation emitted from saidarbitrary point; continuously measuring the surface temperature of saidsteel strip on the basis of said calculated emissivity of the surface ofsaid steel strip and an amount of energy of a reference heat radiationemitted from the surface of a perfect blackbody; and determining a finalangle of reflection (θ) on the surface of said steel strip of said heatradiation emitted from said at least one different point and which hasbeen reflected at least twice between the surface of said steel stripand the surface of said flat reflecting plate, and said prescribed angleof inclination (α) of said reflecting plate with said steel strip, atvalues which satisfy the following limits:

    4°≦θ< 9°                         (A); and

    40°≦θ+2α≦140°      (B).


2. The method as claimed in claim 1, comprising:maintaining said secondinclination angle of said radiation thermometer relative to the surfaceof said steel strip so as to correspond to said final angle ofreflection (θ); said step for continuously measuring said amount ofenergy of said heat radiation from said arbitrary point including;selectivity moving said flat reflecting plate from said prescribedposition thereof to a position at which said heat radiation from said atleast one different point fails to come into said radiation thermometer;and said step for continuously measuring said total sum of said amountsof energy of said heat radiations including: selectively moving saidflat reflecting plate to a prescribed position at which said heatradiation from said at least one different point comes into saidradiation thermometer after having been reflected at least twice bymeans of said reflecting plate.
 3. The method as claimed in claim 1,comprising:maintaining said second inclination angle of said radiationthermometer relative to the surface of said steel strip so as tocorrespond to said final angle of reflection (θ); said step forcontinuously measuring said amount of energy of said heat radiation fromsaid arbitrary point including: selectively rotating said flatreflecting plate from said first inclination angle relative to saidsteel strip to an inclination angle at which said heat radiation fromsaid at least one different point fails to come into said radiationthermometer; and said step for continuously measuring said total sum ofsaid amounts of energy of said heat radiations including: selectivelyrotating said flat reflecting plate to said first inclination angle atwhich said heat radiation from said at least one different point comesinto said radiation thermometer after having been reflected at leasttwice by means of said reflecting plate.
 4. The method as claimed inclaim 1, comprising:maintaining said first inclination angle (α) of saidreflecting plate; said step for continuously measuring said amount ofenergy of said heat radiation of said arbitrary point including:selectively rotating said radiation thermometer from said secondinclination angle thereof to an inclination angle at which said heatradiation from said at least one different point fails to come into saidradiation thermometer; and said step for continously measuring saidtotal sum of said amounts of energy of said heat radiations including:selectively rotating said radiation thermometer to said secondinclination angle at which said heat radiation from said at least onedifferent point comes into said radiation thermometer after having beenreflected at least twice by means of said reflecting plate.
 5. Themethod as claimed in claim 1, comprising:determining said final angle ofreflection (θ) and said first angle of inclination (α) at values whichsatisfy the following limits:

    θ≦-4.5α+87                              (C);

where, 0°≦α≦9°

    θ≧-5α+60                                (D);

where, 0°≦α≦4°

    θ≧4α+24                                 (E); and

where, 4°≦α≦5°

    θ≧0.6+41                                      (F)

where, 5°≦α≦9°; thereby causing said heat radiation from said at leastone different point to reflect at least ten times between the surface ofsaid steel strip and the surface of said flat reflecting plate.
 6. Themethod of claim 5, comprising:maintaining said second inclination angleof said radiation thermometer relative to the surface of said steelstrip so as to correspond to said final angle of reflection (θ); saidstep for continuously measuring said amount of energy of said heatradiation from said arbitrary point including: selectively moving saidflat reflecting plate from said prescribed position thereof to aposition at which said heat radiation from said at least one differentpoint fails to come into said radiation thermometer; and said step forcontinuously measuring said total sum of said amounts of energy of saidheat radiations including: selectively moving said flat reflecting plateto a prescribed position at which said heat radiation from said at leastone different point comes into said radiation thermometer after havingbeen reflected at least twice by means of said reflecting plate.
 7. Themethod of claim 5, comprising:maintaining said second inclination angleof said radiation thermometer relative to the surface of said steelstrip so as to correspond to said final angle of reflection (θ); saidstep for continuously measuring said amount of energy of said heatradiation from said arbitrary point including: selectively rotating saidflat reflecting plate from said first inclination angle relative to saidsteel strip to an inclination angle at which said heat radiation fromsaid at least one different point fails to come into said radiationtheremometer; and said step for continuously measuring said total sum ofsaid amounts of energy of said heat radiations including: selectivelyrotating said flat reflecting plate to said first inclination angle atwhich said heat radiation from said at least one different point comesinto said radiation thermometer after having been reflected at leasttwice by means of said reflecting plate.
 8. The method of claim 5,comprising:maintaining said first inclination angle (α) of saidreflecting plate; said step for continuously measuring said amount ofenergy of said heat radiation of said arbitrary point including:selectively rotating said radiation thermometer from said secondinclination angle thereof to an inclination angle at which said heatradiation from said at least one different point fails to come into saidradiation thermometer; and said step for continuously measuring saidtotal sum of said amounts of energy of said heat radiations including:selectively rotating said radiation thermometer to said secondinclination angle at which said heat radiation from said at least onedifferent point comes into said radiation thermometer after having beenreflected at least twice by means of said reflecting plate.